Results 71 to 80 of about 100,519 (222)

Completeness and Cocompleteness Transfer for Internal Group Objects with Geometric Obstructions

Mathematics
This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects.
Jian-Gang Tang, Nueraminaimu Maihemuti, Jia-Yin Peng, Yimamujiang Aisan, Ai-Li Song   +4 more
doaj   +1 more source

Model category structures on truncated multicomplexes for complex geometry

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4163-4177, December 2025.
Abstract To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to N$N$‐multicomplexes. We present a family of model category structures on the category of N$N$‐multicomplexes where the weak equivalences are the morphisms inducing a quasi‐isomorphism ...
Joana Cirici, Muriel Livernet, Sarah Whitehouse   +2 more
wiley   +1 more source

The shift‐homological spectrum and parametrising kernels of rank functions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird, Jordan Williamson, Alexandra Zvonareva   +2 more
wiley   +1 more source

Completeness and Hereditary Transfer of Exactness Properties for Internal Group Objects in D-Modules

Mathematics
This paper establishes a comprehensive framework for the hereditary transfer of categorical completeness and cocompleteness to categories of internal group objects in D-modules.
Jian-Gang Tang, Miao Liu, Huangrui Lei, Nueraminaimu Maihemuti, Quan-Guo Chen, Jia-Yin Peng   +5 more
doaj   +1 more source

Adjoint functor theorems for $\infty$-categories

, 2018
v1: 21 pages; v2: updated the references, minor changes; v3: 22 pages, changed the terminology from "final" to "coinitial" functors, added three further Corollaries 4.1.5, 5.1.4 and 5.1.5, additional minor changes, accepted for publication in the Journal of the London Mathematical ...
Nguyen, Hoang Kim, Raptis, George, Schrade, Christoph   +2 more
openaire   +3 more sources

Hom ω$\omega$‐categories of a computad are free

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We provide a new description of the hom functor on weak ω$\omega$‐categories, and show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict ω$\omega$‐categories.
Thibaut Benjamin, Ioannis Markakis
wiley   +1 more source

W‐algebras, Gaussian free fields, and g$\mathfrak {g}$‐Dotsenko–Fateev integrals

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract Based on the intrinsic connection between Gaussian free fields and the Heisenberg vertex algebra, we study some aspects of the correspondence between probability theory and W$W$‐algebras. This is first achieved by providing a construction of the W$W$‐algebra associated to a complex simple Lie algebra g$\mathfrak {g}$ by means of Gaussian free ...
Baptiste Cerclé
wiley   +1 more source

GL‐algebras in positive characteristic II: The polynomial ring

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley   +1 more source

Real models for the framed little n$n$‐disks operads

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
wiley   +1 more source

The Gauss-Markov adjunction provides categorical semantics of residuals in supervised learning

Discover Artificial Intelligence
Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI.
Moto Kamiura
doaj   +1 more source